We study contact loci sets of arcs and the behavior of Hironaka's order function defined in constructive Resolution of singularities. We show that this function can be read in terms of the irreducible components of the contact loci sets at a singular point of an algebraic variety.

中文翻译：

---

联系 loci 和 Hironaka 的订单

我们研究弧的接触轨迹集和 Hironaka 阶函数的行为，这些函数在奇异点的构造解析中定义。我们表明，可以根据在代数簇的奇点处的接触轨迹集的不可约分量来读取该函数。